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The task of timetabling is to schedule the trips in a public transport system by determining periodic arrival and departure times at every station. The goal is to provide a service that is both… (More)

- Ralf Borndörfer, Marika Karbstein
- Discrete Optimization
- 2015

We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single… (More)

- Ralf Borndörfer, Heide Hoppmann, Marika Karbstein
- Public Transport
- 2017

The task of periodic timetabling is to schedule the trips in a public transport system by determining arrival and departure times at every station such that travel and transfer times are minimized.… (More)

- Ralf Borndörfer, Marika Karbstein, Marc E. Pfetsch
- Math. Program.
- 2013

The Steiner connectivity problem is a generalization of the Steiner tree problem. It consists in finding a minimum cost set of simple paths to connect a subset of nodes in an undirected graph. We… (More)

Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we… (More)

Given two hypergraphs, representing a fine and a coarse “layer”, and a cycle cover of the nodes of the coarse layer, the cycle embedding problem (CEP) asks for an embedding of the coarse cycles into… (More)

- Ralf Borndörfer, Heide Hoppmann, +5 authors Niels Lindner
- 2018

Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we… (More)

- Ralf Borndörfer, Nam-Dung Hoang, +7 authors Alexander Martin
- 2013

Steiner trees are constructed to connect a set of terminal nodes in a graph. This basic version of the Steiner tree problem is idealized, but it can effectively guide the search for successful… (More)

We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single… (More)

- Ralf Borndörfer, Marika Karbstein
- Networks
- 2018

This paper presents an approximation algorithm for the Steiner connectivity problem, which is a generalization of the Steiner tree problem that involves paths instead of edges. The problem can also… (More)